SAINT-VENANTEND EFFECTS FOR PLANE DEFORMATIONS OF ELASTIC COMPOSITES
Title:
SAINT-VENANTEND EFFECTS FOR PLANE DEFORMATIONS OF ELASTIC COMPOSITES
Author:
Miller, K. L. Horgan, C. O.
Appeared in:
Mechanics of advanced materials & structures
Paging:
Volume 2 (1995) nr. 3 pages 203-214
Year:
1995-09-01
Contents:
In the linear theory of elasticity, Saint-Venant's principle is used to justify the neglect of edge effects when determining stresses in a body. For isotropic materials, the validity of this is well established. However, for anisotropic and composite materials, experimental results have shown that edge effects may persist much farther into the material than for isotropic materials and as a result cannot be neglected. This paper provides a further analysis of the effects of material anisotropy on the exponential decay rate for stresses in a semi-infinite elastic strip. A linearly elastic semi-infinite strip in a state of plane stress/strain subject to a self-equilibrated end load is considered first for a specially orthotropic material and then for the general anisotropic material. The problem is governed by a fourth-order elliptic partial differential equation with constant coefficients. In the former case just a single dimension-less material parameter appears, while in the latter, only three dimensionless parameters are required. The exact stress decay rate, characterized in terms of the eigenvalues of a fourth-order ordinary differential equation, is computed numerically for a variety of contemporary engineering materials, both for specially orthotropic and anisotropic materials. The influence of the off-axis constants is examined. Results of the type obtained here have several important practical applications. For example, they provide physical insight into the mechanical testing of anisotropic and laminated composite structures, are useful in assessing the influence of fasteners, joints, etc. on the behaviour of composite structures and allow for 'tailoring' a material with specific properties to ensure that local stresses attenuate at a desired rate. The results also apply to laminates and composite plates under edge loading.
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